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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 373 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the 11th term of the AP 14, 16, 18, 20, …? (a) 36 (b) 20 (c) 22 (d) 34
  2. 2.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 279 (b) 252 (c) 52 (d) 504
  3. 3.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 200 (c) 380 (d) 28
  4. 4.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 15 (b) 19 (c) 16 (d) 14
  5. 5.What is the 25th term of the AP 9, 15, 21, 27, …? (a) 159 (b) 144 (c) 153 (d) 150
  6. 6.What is the 28th term of the AP 4, 10, 16, 22, …? (a) 168 (b) 172 (c) 166 (d) 162
  7. 7.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 81 (c) 90 (d) 17
  8. 8.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 300 (b) 40 (c) 564 (d) 282
  9. 9.What is the 10th term of the AP 10, 15, 20, 25, …? (a) 60 (b) 55 (c) 50 (d) 45
  10. 10.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 240 (d) 120
  11. 11.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 31 (c) 95 (d) 110
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 11 (d) 21
  13. 13.What is the 36th term of the AP 12, 18, 24, 30, …? (a) 222 (b) 228 (c) 210 (d) 216
  14. 14.What is the 31st term of the AP 3, 7, 11, 15, …? (a) 123 (b) 124 (c) 127 (d) 120
  15. 15.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 102 (b) 106 (c) 99 (d) 103
  16. 16.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 171 (d) 162
  17. 17.Which term of the AP 7, 16, 25, 34, … is 331? (a) 38th (b) 37th (c) 36th (d) 39th
  18. 18.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 120 (c) 60 (d) 22
  19. 19.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 265 (b) 290 (c) 530 (d) 49
  20. 20.Which term of the AP 3, 7, 11, 15, … is 131? (a) 32nd (b) 34th (c) 35th (d) 33rd
  21. 21.What is the 29th term of the AP 13, 18, 23, 28, …? (a) 153 (b) 145 (c) 140 (d) 158
  22. 22.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 31 (c) 32 (d) 38
  23. 23.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
  24. 24.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 54 (c) 48 (d) 96
  25. 25.What is the 30th term of the AP 4, 7, 10, 13, …? (a) 91 (b) 94 (c) 87 (d) 90
  26. 26.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 129 (b) 126 (c) 122 (d) 119
  27. 27.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 11 (b) 12 (c) 13 (d) 15
  28. 28.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 325 (c) 650 (d) 350
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  31. 31.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 252 (c) 240 (d) 480
  32. 32.Which term of the AP 1, 3, 5, 7, … is 23? (a) 11th (b) 12th (c) 13th (d) 14th
  33. 33.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 144 (c) 80 (d) 72
  34. 34.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 17 (c) 18 (d) 20
  35. 35.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 9 (c) 7 (d) 6
  36. 36.What is the 22nd term of the AP 11, 17, 23, 29, …? (a) 132 (b) 126 (c) 137 (d) 143
  37. 37.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 143 (b) 154 (c) 286 (d) 23
  38. 38.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1770 (c) 3540 (d) 1711
  39. 39.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 7 (c) 10 (d) 6
  40. 40.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 310 (b) 155 (c) 29 (d) 170

Answer key

  1. 34
  2. 252
  3. 190
  4. 15
  5. 153
  6. 166
  7. 81
  8. 282
  9. 55
  10. 120
  11. 95
  12. 36
  13. 222
  14. 123
  15. 103
  16. 171
  17. 37th
  18. 60
  19. 265
  20. 33rd
  21. 153
  22. 31
  23. 441
  24. 48
  25. 91
  26. 122
  27. 12
  28. 325
  29. 625
  30. 361
  31. 240
  32. 12th
  33. 72
  34. 17
  35. 7
  36. 137
  37. 143
  38. 1770
  39. 6
  40. 155

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